A communication may be arranged in the form of a frame comprising a preamble for synchronisation followed by a data payload. The preamble may comprise multiple repetitions of a synchronisation word that is known to the receiver. To detect the start of the frame, the receiver has to detect this repeated pattern in the presence of noise. The receiver typically does not have prior knowledge of the frequency error between it and the transmitter or of the channel impulse response. The benefits of accurate and fast detection of the start of the frame include allowing the system to reduce the length of the preamble required in each frame, allowing the receiver to dedicate more of the received preamble data to frequency or channel estimation and improving the overall detection rate.
The goal of the preamble detection is to detect when a frame is present, i.e. when a channel exists at the output of the correlator. In one method, the received samples are initially correlated with the synchronisation word. An example output of this stage is shown in FIG. 1, where z is the output of the correlator. Some lags will generate peaks in the correlator output. In FIG. 1, a lag of 5 samples generates the highest peaks. The synchronisation word is L samples long, and therefore the peak repeats itself every L samples. Each of these peaks represents an estimate of the channel impulse response.
FIG. 1 illustrates an example of a correlator output when there is no frequency error between the transmitter and the receiver and the channel does not change significantly over the length of the preamble. Consequently the peaks repeat themselves at a regular spacing of L samples. In practical systems there may be a frequency error between transmitter and receiver, which is unknown to the receiver. In this case the channel impulse response is still repeated, but with an unknown phase shift across the synchronisation words.
Without an accurate estimate of the frequency offset, it is very difficult for the receiver to demodulate the transmitted data correctly. The accumulating rotation in the symbol constellation can result in significant errors. It is therefore important to estimate the frequency offset accurately. Typically, this is achieved by examining the received preamble and finding the rate of change of the complex angle between the symbols in that preamble.
Existing schemes for estimating the frequency offset either limit the frequency capture range, are computationally intensive or do not perform well at low signal to noise ratios (SNR). Simpler estimators in particular tend to suffer at low SNR due to noise affecting the angle estimation. Noise at the input to the arctangent function (which is an important operation in the frequency offset estimation) causes the output of the arctangent function to be almost uniformly distributed between +/−π at low SNR (at high SNR it is approximately Gaussian distributed about the expected angle of the input signal). This means it can be very difficult to estimate the offset accurately at low SNR.
Therefore, an improved method for estimating a frequency offset is required.